Commit 567feeb5 authored by Erik Fransson's avatar Erik Fransson

updated figs

parent 0b559420
...@@ -5,7 +5,7 @@ Liquid and solid aluminum ...@@ -5,7 +5,7 @@ Liquid and solid aluminum
In this first example aluminium will be studied. An EAM potential was In this first example aluminium will be studied. An EAM potential was
used [Phys. Rev. B 59, 3393 (1999)] to describe both the solid and used [Phys. Rev. B 59, 3393 (1999)] to describe both the solid and
liquid phases. The melting point was found to be about 930 K. The liquid phases. The melting point was found to be about 1000 K. The
lattice parameters used for the NVT MD simulations were found running lattice parameters used for the NVT MD simulations were found running
NPT and averaging the box length. NPT and averaging the box length.
...@@ -31,8 +31,8 @@ below if running the :program:`dynasor` scripts as are. ...@@ -31,8 +31,8 @@ below if running the :program:`dynasor` scripts as are.
In the figure the structure factor :math:`S(q)` is shown. In the figure the structure factor :math:`S(q)` is shown.
.. figure:: figs/Al_liquid/Al_liquid_static.png .. figure:: figs/Al_liquid/Al_liquid_Sq.png
:scale: 120 % :scale: 15 %
:align: center :align: center
Structure factor :math:`S(q)` computed by running Structure factor :math:`S(q)` computed by running
...@@ -58,7 +58,7 @@ Figure 3 of :cite:`Mokshin`. The clear dispersion in ...@@ -58,7 +58,7 @@ Figure 3 of :cite:`Mokshin`. The clear dispersion in
of :cite:`Mokshin`. of :cite:`Mokshin`.
.. figure:: figs/Al_liquid/Al_liquid_heatmap.png .. figure:: figs/Al_liquid/Al_liquid_heatmap.png
:scale: 120 % :scale: 100 %
:align: center :align: center
Dynamical structure factor (a), longitudinal current (b) and Dynamical structure factor (a), longitudinal current (b) and
...@@ -73,51 +73,35 @@ of :cite:`Mokshin`. ...@@ -73,51 +73,35 @@ of :cite:`Mokshin`.
Crystalline Crystalline
=========== ===========
.. todo:: In this example we look at alumnium (FCC) below the melting
Update these old figures. point at :math:`T=300K`. Since the sampling along a path is much faster than
doing a spherical average the number of atoms used here is 6912 (12x12x12 fcc).
In this example we look at alumnium below the melting
point at :math:`T=300K`. The crystal structure is face-centered-cubic
(fcc) and :math:`q`-space sampling was done along three paths
.. math:: L=\frac{2\pi}{a}
\Big(\frac{1}{2},\frac{1}{2},\frac{1}{2}\Big) \quad , \quad
K=\frac{2\pi}{a} \Big(\frac{3}{4},\frac{3}{4},0\Big)
Since the sampling along a path is much faster than doing a spherical
average the number of atoms used here is 6912 (12x12x12 fcc).
The transverse and longitudinal current correlation is shown both in The transverse and longitudinal current correlation is shown both in
time and frequency between :math:`\Gamma` and K. Here the time and frequency for a single q-point. Fits to the analytical functions
:math:`q`-value is between 0 and 1 and represent how far along the are also shown.
path you are.
.. figure:: figs/Al_solid/C_ktw_GK.png .. figure:: figs/Al_solid/fit_illustration.png
:scale: 50 % :scale: 80 %
:align: center :align: center
Current correlations between :math:`\Gamma` and K in both time Longitudinal and transverse current correlations in both time and frequency.
(top) and frequency .
Looking at the current correlations in time we see that the Looking at the current correlations in time we see that the
longitudinal is oscillating with one frequency and the transverse with longitudinal is oscillating with one frequency and the transverse with
many. This agrees with what is seen in the frequency domain. two. This agrees with what is seen in the frequency domain.
The sum of the longitudinal and transverse current correlation is seen The sum of the longitudinal and transverse current correlation is seen
below together with the phonon dispersion calculated, using the same below together with the phonon dispersion calculated, using the same
potential, by phonopy. potential, by phonopy.
.. figure:: figs/Al_solid/dispersion_T300.png .. figure:: figs/Al_solid/current_heatmap_T300.png
:scale: 50 % :scale: 70 %
:align: center :align: center
Sum of the longitudinal and transverse current show along the path Sum of the longitudinal and transverse current heatmaps.
L to :math:`\Gamma` to K. The black dots indicate the results from
phonopy calculations.
The agreement with the phonon dispersion calculated with phonopy is The agreement with the phonon dispersion calculated with phonopy is
very good. The fact that there is discrete :math:`q`-values which give very good. The fact that there is discrete :math:`q`-values which give
rise to high intensitiy is due to the finite supercell size not rise to high intensitiy is due to the finite supercell size not
supporting all kinds of oscillations. supporting all kinds of oscillations.
This diff is collapsed.
This diff is collapsed.
...@@ -12,8 +12,6 @@ from Lewis and Singer (1974). The melting point was found to be about ...@@ -12,8 +12,6 @@ from Lewis and Singer (1974). The melting point was found to be about
1300 K and the simulations were carried out at 1400 K for 4096 atoms 1300 K and the simulations were carried out at 1400 K for 4096 atoms
(:math:`8\times8\times8` conventional unit cells). (:math:`8\times8\times8` conventional unit cells).
.. todo::
Insert proper reference via `references.bib`.
The partial correlation functions are denoted :math:`S_{AA}(q,\omega)` The partial correlation functions are denoted :math:`S_{AA}(q,\omega)`
where :math:`A` is an atomic species and :math:`S` represents an where :math:`A` is an atomic species and :math:`S` represents an
...@@ -41,86 +39,36 @@ combination of the partial functions weighted with the appropriate ...@@ -41,86 +39,36 @@ combination of the partial functions weighted with the appropriate
atomic form factors. atomic form factors.
Structure factors: F(q,t) and S(q,w) Structure factors: F(q,t)
==================================== =========================
The figure below shows the static structure factors. The figure below shows the static charge and mass structure factors.
.. figure:: figs/NaCl_liquid/structureFactor.png .. figure:: figs/NaCl_liquid/NaCl_Sq.png
:scale: 50 % :scale: 40 %
:align: center :align: center
Number-number and charge-charge structure factor (left) and the static charge and mass structure factors.
partial structure factors (right).
All structure factors agree well with Figures 10.2 and 10.3 in All structure factors agree well with Figures 10.2 and 10.3 in
:cite:`HansenMcDonald`. The normalization differs by a factor of two, :cite:`HansenMcDonald`.
which is simply a matter of choice if the normalization for the
partial structure factor should be done with :math:`N_A` or
:math:`N_A+N_B`.
Below the partial intermediate scattering functions and dynamical Current correlations: C(q,w)
structure factors are shown. ============================
.. figure:: figs/NaCl_liquid/S_partial.png
:scale: 50 %
:align: center
Partial :math:`F(q,t)` and :math:`S(q,\omega)` for two different
**q**-values.
.. figure:: figs/NaCl_liquid/S_CMN.png
:scale: 50 %
:align: center
Mass charge and number computed from partial :math:`F(q,t)` and
:math:`S(q,\omega)`. Note the logged scale for :math:`S(q,\omega)`
in order to resolve some peaks.
.. figure:: figs/NaCl_liquid/S_partial_map.png
:scale: 50 %
:align: center
Map of logged partial dynamical structure factors.
.. figure:: figs/NaCl_liquid/S_CMN_map.png
:scale: 50 %
:align: center
Map of logged charge, mass and number dynamical structure factors.
Charge correlation: C(q,t) and C(q,w)
=====================================
Below the partial, charge, mass and number longitudinal and transverse Below the partial, charge, mass and number longitudinal and transverse
current correlation functions are shown. Note that the peaks in the current correlation functions are shown.
frequency domain are much more easily seen compared to the dynamical
structure factors. These figures show four modes (TA, TO, LA, LO).
.. figure:: figs/NaCl_liquid/C_partial.png
:scale: 50 %
:align: center
Partial current correlations :math:`C(q,t)` and :math:`C(q,\omega)`.
.. figure:: figs/NaCl_liquid/C_CMN.png
:scale: 50 %
:align: center
Mass, charge and number current correlations :math:`C(q,t)` and
:math:`C(q,\omega)`.
Below maps of the current correlations are shown.
.. figure:: figs/NaCl_liquid/C_partial_map.png .. figure:: figs/NaCl_liquid/NaCl_partial_heatmaps.png
:scale: 50 % :scale: 40 %
:align: center :align: center
Map of partial current correlations. Heatmap of partial current correlations. Top is longitudinal and bottom
is transverse.
.. figure:: figs/NaCl_liquid/C_CMN_map.png .. figure:: figs/NaCl_liquid/NaCl_charge_mass_heatmaps.png
:scale: 50 % :scale: 40 %
:align: center :align: center
Map of current, mass and number current correlations. Heatmap of charge and mass current correlations. Top is longitudinal and
bottom is transverse.
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